Nonlinear Dynamics from Linear Quantum Evolutions

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61988987%3A17310%2F19%3AA200232C" target="_blank" >RIV/61988987:17310/19:A200232C - isvavai.cz</a>

Výsledek na webu

<a href="https://www.sciencedirect.com/science/article/abs/pii/S000349161930212X" target="_blank" >https://www.sciencedirect.com/science/article/abs/pii/S000349161930212X</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.aop.2019.167957" target="_blank" >10.1016/j.aop.2019.167957</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Nonlinear Dynamics from Linear Quantum Evolutions

Popis výsledku v původním jazyce

Linear dynamics restricted to invariant submanifolds generally gives rise to nonlinear dynamics. Submanifolds in the quantum framework may emerge for several reasons: one could be interested in specific properties possessed by a given family of states, either as a consequence of experimental constraints or inside an approximation scheme. In this work we investigate such issues in connection with a one parameter group ϕt of transformations on a Hilbert space, H, defining the unitary evolutions of a chosen quantum system. Two procedures will be presented: the first one consists in the restriction of the vector field associated with the Schrödinger equation to a submanifold invariant under the flow ϕt. The second one makes use of the Lagrangian formalism and can be extended also to non-invariant submanifolds, even if in such a case the resulting dynamics is only an approximation of the flow ϕt. Such a result, therefore, should be conceived as a generalization of the variational method already employed for stationary problems.

Název v anglickém jazyce

Nonlinear Dynamics from Linear Quantum Evolutions

Popis výsledku anglicky

Linear dynamics restricted to invariant submanifolds generally gives rise to nonlinear dynamics. Submanifolds in the quantum framework may emerge for several reasons: one could be interested in specific properties possessed by a given family of states, either as a consequence of experimental constraints or inside an approximation scheme. In this work we investigate such issues in connection with a one parameter group ϕt of transformations on a Hilbert space, H, defining the unitary evolutions of a chosen quantum system. Two procedures will be presented: the first one consists in the restriction of the vector field associated with the Schrödinger equation to a submanifold invariant under the flow ϕt. The second one makes use of the Lagrangian formalism and can be extended also to non-invariant submanifolds, even if in such a case the resulting dynamics is only an approximation of the flow ϕt. Such a result, therefore, should be conceived as a generalization of the variational method already employed for stationary problems.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2019

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

ANN PHYS-NEW YORK

ISSN

0003-4916

e-ISSN

—

Svazek periodika

411

Číslo periodika v rámci svazku

December 2019

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

38

Strana od-do

167957

Kód UT WoS článku

000502886800016

EID výsledku v databázi Scopus

2-s2.0-85073540485